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Prove: (tan theta)/(sec theta-1)=(tan th...

Prove: `(tan theta)/(sec theta-1)=(tan theta+sec theta+1)/(tan theta+sec theta-1)`

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`1 + tan^2 theta = sec^2 theta`
`therefore tan^2 = sec^2 theta-1` ltbgt `therefore tan theta xx tan theta = (sec theta +1 )(sec theta - 1)`
`therefore (tan theta)/((sec theta - 1)) = ((sec theta + 1))/(tan theta) `
By therorem on equal rations,
`(tan theta)/((sec theta -1)) = ((sec theta + 1))/(tan theta)=(tan theta + sec theta +1)/(sec theta -1 + tan theta)`
` therefore (tan theta)/(sec theta -1) = (tan theta + sec theta +1)/(tan theta + sec theta -1)`
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